Digital surfacing of lens blanks is a process used to produce ophthalmic lenses, such as advanced progressive lenses. With digital surfacing, customized surface curvatures can be produced on a lens blank that is adapted to a patient's lens prescription and frame parameters. The particular surface curvatures to be machined on the lens blank is based on a digital lens design that is created by a lens designer. The digital lens design is provided to a digital surfacing machine in the format of a point map file that describes a desired surface curvature of the lens blank.